The southwest corner of a football field is selected as the origin of a rectangular coordinate system. A football is placed on the field at (x, y) = (37.7 m, 62.2 m). How long would it take a student, walking at a speed of 1.93 m/s, directly from the corner towards the football, to reach it?
Well, it seems like we have a classic case of "chasing the football" here! Let's calculate how long it would take that student to reach the football.
To find the distance between the corner and the football, we need to use the Pythagorean theorem. The horizontal distance (x-distance) between the corner and the football is 37.7 m, and the vertical distance (y-distance) is 62.2 m.
So, using a^2 + b^2 = c^2, we can find the diagonal distance (c-distance) between the corner and the football:
c = √(37.7^2 + 62.2^2)
c ≈ 73.66 m
Now, to find how long it would take the student to reach the football, we divide the distance by the student's walking speed:
time = distance / speed
time = 73.66 m / 1.93 m/s
time ≈ 38.16 seconds
So, it would take the student approximately 38.16 seconds to reach the football. Just make sure they don't trip over their shoelaces on the way!
To find the time it would take for a student to reach the football, we need to calculate the distance between the southwest corner and the football and divide it by the student's walking speed.
First, let's calculate the distance using the coordinates of the southwest corner (origin) and the coordinates of the football.
Using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) are the coordinates of the southwest corner (origin) and (x2, y2) are the coordinates of the football.
Given:
(x1, y1) = (0 m, 0 m)
(x2, y2) = (37.7 m, 62.2 m)
So, the distance between the southwest corner and the football is:
Distance = √((37.7 m - 0 m)^2 + (62.2 m - 0 m)^2)
= √(37.7^2 + 62.2^2)
= √(1420.29 + 3864.84)
= √5285.13
= 72.73 m (approximately, rounded to two decimal places)
Now, to find the time it would take for the student to reach the football, we divide the distance by the student's walking speed:
Time = Distance / Speed
= 72.73 m / 1.93 m/s
≈ 37.70 seconds (approximately, rounded to two decimal places)
Therefore, it would take approximately 37.70 seconds for the student, walking at a speed of 1.93 m/s, to reach the football directly from the southwest corner of the field.